Definition:Orthonormal Subset
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Definition
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space.
Let $S \subseteq V$ be a subset of $V$.
Then $S$ is an orthonormal subset if and only if:
- $(1): \quad \forall u \in S: \norm u = 1$
where $\norm {\, \cdot \,}$ is the inner product norm.
- $(2): \quad S$ is an orthogonal set:
- $\forall u, v \in S: u \ne v \implies \innerprod u v = 0$
Also see
Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $I.4.1$